" a VNC-like interface is required to enter disk encryption password, which could be intercepted by the host. "
There's a rule in security that anyone in physical possession of your device should be assumed to have access to it. The host has the server whether physical or virtual. You're not safe from them. Trusting them is the tradeoff made for the cheap, hosted server.
" I look at dedicated box more as an upgrade from VPS."
Multiple VPS's share a physical box. A malicious VPS can look for secrets in another VPS using side channels. This isn't possible on bare metal: they have to compromise an app or get a shell first. The next concern would be endpoint security. OpenBSD covers that well. Then, there's host or peripheral firmware which is almost always a risk if a 3rd party is hosting things. Your attack surface does go down, though, when you're not sharing a box with an attacker. There's also the performance benefits.